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F á dS directly as a surface integral Then verify thatF = curl(A ),whereA = (0,x,xz)and evaluate the surface integral again using StokesÕTheorem 19 LetA be the vector potential andB the magnetic Þeld of the inÞnite solenoid of radiusR in Example 4 Use StokesÕTheorem to compute (a) The ßux of B through a circle in thexyplane of radiusr. 6\dmc rqyv tmc rt\gf gi\cokpgo '\kg 6wurqd =dgdqlh dfádz z\srzldgdm f vl r &h qlnx l 5hmhqflh x *\á virupxárzdqld 7\fk gzyfk oxgl. *& `R hb @ `' , ;.

TableCaption TABLE 13 A useful collection of symbolsJؽâ $marker2> $paratextti Title> 8$paratexth1 Heading1,a1 Appendix1,h1n Heading1 NoNum. Solution f x = 12x 212xy, f y = 6x 2 6y, Thus, 12x 2 = 12xy and 6x 2 = 6y Since x 2 = xy, x = 0 or x = y If x = 0, then x 2 = y implies that y = 0, and the critical point is (0,0) If x = y, then x 2 = y implies that x 2 = x or x = 1,0 Thus, the critical points are ( 0,0) and ( 1,1) However,.